4x+3=x+2(x+7)x=

Solution for 4x+3=x+2(x+7)x= equation:

4x+3=x+2(x+7)x=

We move all terms to the left:

4x+3-(x+2(x+7)x)=0


We calculate terms in parentheses: -(x+2(x+7)x), so:

x+2(x+7)x

We multiply parentheses

2x^2+x+14x

We add all the numbers together, and all the variables

2x^2+15x

Back to the equation:

-(2x^2+15x)


We get rid of parentheses

-2x^2+4x-15x+3=0

We add all the numbers together, and all the variables

-2x^2-11x+3=0

a = -2; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·(-2)·3
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{145}}{2*-2}=\frac{11-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*-2}=\frac{11+\sqrt{145}}{-4}
$